Pseudo Zero Vectors for Space Vector Modulation and Enhanced Space Vector Modulation

ABSTRACT

A method of performing space vector modulation for PWM control for creating AC waveforms includes generating and sampling a reference signal to generate reference samples and performing a reference vector approximation to synthesize a reference vector associated with at least one of the reference samples. The reference vector approximation employs active vectors, one or more zero vectors, and one or more pseudo zero vectors in the formation thereof. Another method of performing space vector modulation (SVM) includes generating a reference signal and sampling the reference signal at a sampling frequency to generate a plurality of reference samples. The method also includes performing a reference vector approximation to synthesize a reference vector associated with at least one of the reference samples, wherein the reference vector approximation has a first portion that employs two adjacent active vectors and a remaining portion that employs two non-adjacent active vectors in the formation thereof.

FIELD

The present disclosure relates to an apparatus and method for performingspace vector modulation for PWM control for creating AC waveforms usingpseudo zero vectors or enhanced space vector modulation, or both, forexample, in motor control applications.

BACKGROUND

Space vector modulation (SVM) is an algorithm for the control of pulsewidth modulation (PWM). It is used for the creation of alternatingcurrent (AC) waveforms; most commonly to drive three-phase AC poweredmotors at varying speeds from DC. There are numerous variations of SVMthat result in different quality and computational requirements.

A three phase inverter 100 as shown in FIG. 1 must be controlled so thatat no time are both switches in the same leg turned on or else the DCsupply would be shorted. This requirement may be met by thecomplementary operation of the switches within a leg. That is, if A⁺ ison, then A⁻ is off, and vice versa. This leads to eight possibleswitching vectors for the inverter 100, V₀ through V₇ with six activeswitching vectors and two zero vectors, as illustrated in the chart 110of FIG. 2.

To implement space vector modulation a reference signal V_(ref) issampled with a frequency f_(s) (T_(s)=1/f_(s)). The reference signal maybe generated from three separate phase references using the αβγtransform, for example. The reference vector is then synthesized using acombination of the two adjacent active switching vectors and one or bothof the zero vectors. Various strategies of selecting the order of thevectors and which zero vector(s) to use exist. Strategic selection ofthe vectors will affect the harmonic content and the switching losses.

SUMMARY

The present disclosure is directed to a method of performing spacevector modulation for PWM control for creating AC waveforms. The methodincludes generating and sampling a reference signal to generatereference samples and performing a reference vector approximation tosynthesize a reference vector associated with at least one of thereference samples. The reference vector approximation employs activevectors, one or more zero vectors, and one or more pseudo zero vectorsin the formation thereof.

In one embodiment of the method, the pseudo vector comprises acombination of two active vectors that have an angle differencetherebetween of 180°. In another embodiment, the two active vectors thatin combination form the pseudo vector have a scalar amplitude that isthe same.

In another embodiment of the method, the pseudo vector comprises acombination of three active vectors that have an angle differencetherebetween of 120°. In still another embodiment, the three activevectors that in combination form the pseudo vector have a scalaramplitude that is the same.

In one embodiment of the method, the active vectors in the referencevector approximation comprise adjacent active vectors. In anotherembodiment, a portion of the reference vector is approximated by twoadjacent active vectors, and a remaining portion of the reference vectoris approximated by two non-adjacent active vectors. In accordance withone embodiment, the portion of the reference vector driven by activevectors is represented by a variable m, wherein 0≦m≦1, and the remainingportion of the reference vector driven by active vectors is representedby 1−m. When m=1, the entire reference vector driven by active vectorsis approximated by two adjacent vectors, and when m=0 the entirereference vector driven by active vectors is approximated by twonon-adjacent active vectors. In one embodiment, the non-adjacent activevectors are separated from one another by 120°.

In accordance with another embodiment of the disclosure, a controlsystem comprises a space vector modulator configured to receive aplurality of reference signal samples and perform a reference vectorapproximation to synthesize a reference vector associated with at leastone of the reference signal samples. The reference vector approximationemploys active vectors, one or more zero vectors, and one or more pseudozero vectors in the formation thereof, wherein the space vectormodulator outputs timing signals based on the reference vectorapproximation. The control system further comprises a pulse widthmodulation unit configured to receive the timing signals from the spacevector modulator, and output pulse width modulation control signalsbased thereon, and a three phase inverter configured to receive thepulse width modulation control signals and generate alternating currentwaveforms based thereon.

In one embodiment of the control system a pseudo vector comprises acombination of two active vectors that have an angle differencetherebetween of 180°. In another embodiment, the two active vectors thatin combination form the pseudo vector have a scalar amplitude that isthe same.

In another embodiment of the control system a pseudo vector comprises acombination of three active vectors that have an angle differencetherebetween of 120°. In still another embodiment, the three activevectors that in combination form the pseudo vector have a scalaramplitude that is the same.

In one embodiment of the control system the active vectors in thereference vector approximation comprise adjacent active vectors. Inanother embodiment, a portion of the reference vector is approximated bytwo adjacent active vectors, and a remaining portion of the referencevector is approximated by two non-adjacent active vectors. In oneembodiment, the portion of the reference vector is represented by avariable m, wherein 0≦m≦1, wherein the remaining portion of thereference vector is represented by 1−m. When m=1 the entire referencevector driven by active vectors is approximated by two adjacent activevectors, and when m=0 the entire reference vector driven by activevectors is approximated by two non-adjacent active vectors. In oneembodiment, the non-adjacent vectors are separated from one another by120°.

In one embodiment of the control system the three phase invertercomprises a first series-connected switch pair connected together at anode that forms a first phase output, a second series-connected switchpair connected together at a node that forms a second phase output, anda third series-connected switch pair connected together at a node thatforms a third phase output. The inverter further comprises a shuntresistor connected with a first terminal to a bottom node of each of thefirst, second and third series-connected switch pairs, and a secondterminal coupled to a reference potential, and an amplifier having firstand second inputs coupled to the first and second terminals of the shuntresistor, respectively, wherein an output of the amplifier reflects acurrent level conducting through the shunt resistor.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments according to the disclosure will be explained inmore detail in the following text with reference to the attachedfigures, in which:

FIG. 1 is a schematic diagram of a three phase inverter for generatingAC waveforms;

FIG. 2 is a chart illustrating various vectors for switching theswitches of the three phase inverter of FIG. 1;

FIG. 3 is hexagon diagram illustrating the basic voltage space vectorsfrom the chart of FIG. 2;

FIG. 4 is a hexagon diagram illustrating a reference vectorapproximation in accordance with conventional techniques;

FIG. 5 is a graph illustrating normalized time versus reference vectorangle for conventional space vector modulation (SVM);

FIGS. 6A-6E are hexagon diagrams illustrating a basic pseudo zerovector, wherein FIGS. 6A-6C show a combination of two active vectors,and FIGS. 6D-6E show a combination of three active vectors;

FIGS. 7A-7B show approximations of a reference vector using one pseudozero vector, such as those illustrated in FIGS. 6A-6C according to oneembodiment;

FIG. 8 shows an approximation of a reference vector using two pseudozero vectors, such as those illustrated in FIGS. 6A-6C according to oneembodiment;

FIG. 9 is a graph illustrating a maximum inverter DC link voltageutilization versus A for a reference vector in accordance with theembodiment of FIGS. 7A-7B;

FIG. 10 is a graph illustrating normalized time versus reference vectorangle for conventional space vector modulation (SVM) with use of pseudozero vectors such as that shown in FIGS. 7A-7B according to oneembodiment;

FIG. 11 is a graph illustrating a maximum inverter DC link voltageutilization versus A for a reference vector in accordance with theembodiment of FIG. 8;

FIG. 12 is a graph illustrating normalized time versus reference vectorangle for conventional space vector modulation (SVM) with use of pseudozero vectors such as that shown in FIG. 8 according to one embodiment;

FIGS. 13A-13B are block diagrams illustrating a control system, such asa motor control system, that employs a space vector modulator thatemploys pseudo zero vectors in approximating reference vectors accordingto one embodiment of the disclosure;

FIG. 14 is a space vector hexagon showing a reference vector in polarcoordinates and Cartesian coordinates, respectively;

FIG. 15 is a block diagram illustrating a three phase inverter in acontrol system such as that illustrated in FIGS. 13A-13B that employssingle-shunt current sensing according to one embodiment;

FIGS. 16A-16B illustrate examples of 5-segment switching sequences forthe example of FIGS. 7A-7B;

FIGS. 17A-17B illustrate examples of 5-segment switching sequences forthe example of FIG. 8;

FIGS. 18A-18B illustrate examples of 6-segment switching sequences forthe example of FIG. 8;

FIGS. 19A-19B illustrate examples of 7-segment switching sequences forthe example of FIG. 8;

FIG. 20 illustrates the DC link current corresponding to the switchingsequences shown in FIG. 18A;

FIG. 21 is a space vector hexagon illustrating an alternative referencevector approximation with one pseudo zero vector according to oneembodiment;

FIGS. 22A-22B are space vector hexagons illustrating a reference vectorapproximation employing enhanced SVM that utilizes three adjacent activevectors according to one embodiment of the disclosure;

FIGS. 23A-23B are space vector hexagons illustrating a reference vectorapproximation employing enhanced SVM under the condition where m=0 suchthat the reference vector is approximated solely by non-adjacent activevectors in accordance with one embodiment;

FIG. 24 is a graph illustrating a maximum inverter DC ling voltageutilization versus m for enhanced SVM in accordance with one embodimentof the disclosure;

FIGS. 25A-25B are graphs illustrating normalized time versus referenceangle plots for enhanced SVM at m=0.8 and m=0.2, respectively, accordingto one embodiment;

FIG. 26 is a graph illustrating a normalized time versus reference angleplot for enhanced SVM at m=0 according to one embodiment;

FIGS. 27A-27B are block diagrams illustrating a control system, such asa motor control system, that employs enhanced SVM that may includenon-adjacent active vectors in approximating reference vectors accordingto one embodiment of the disclosure;

FIG. 28 is a space vector hexagon showing a reference vector in enhancedSVM in polar coordinates and Cartesian coordinates, respectively;

FIG. 29 is a block diagram illustrating a three phase inverter in acontrol system such as that illustrated in FIGS. 27A-27B that employssingle-shunt current sensing according to one embodiment;

FIGS. 30A-30B illustrate examples of 4-segment switching sequences forenhanced SVM according to one embodiment;

FIGS. 31A-31B illustrate examples of 6-segment switching sequences forenhanced SVM according to one embodiment;

FIGS. 32A-32B illustrate examples of 3-segment switching sequences forenhanced SVM at m=0 according to one embodiment;

FIGS. 33A-33B illustrate examples of 5-segment switching sequences forenhanced SVM at m=0 according to one embodiment;

FIG. 34 illustrates the DC link current corresponding to the switchingsequences shown in FIG. 31A;

FIGS. 35A-35B are space vector hexagons illustrating special cases ofenhanced SVM, wherein FIG. 35A illustrates the case of m≧1, and FIG. 35Billustrates the case of m≦0, wherein four active vectors are employed toapproximate the reference vector, wherein FIG. 35A shows adjacent activevectors and FIG. 35B shows non-adjacent active vectors.

DETAILED DESCRIPTION

In some cases, the same reference symbols are used in the following textfor objects and functional units that have the same or similarfunctional characteristics. Furthermore, optional features of thevarious example embodiments can be combined with one another or replacedby one another.

For industry and automotive motor control applications, SVM isubiquitously used in the sinusoidal commutation control (such as V/f,FOC (field oriented control), and DTC (direct torque control)) of PMSM(permanent magnet synchronous motor) and ACIM (alternating currentinduction motor) to generate sine waveforms from three-phase inverters.Sinusoidal commutation motor control with a single-shunt current sensingresistor inserted in the inverter DC link is a desirable solution whencompared to dual-shunt and triple-shunt current sensing techniques,owing to its important advantages such as low cost, simplicity and etc.However, two current samples within one pulse width modulation (PWM)cycle are needed for correct motor phase current reconstruction withsingle-shunt current sensing. However, with conventional SVM techniques,the accurate current construction is difficult in the followingsituations: (1) The reference voltage space vector is crossing a sectorborder as only one current sample can be measured (this occurs in manyinstances) and (2) When the modulation index is low and the samplingintervals are too short, none of the current samples can be taken (thisnormally happens in ultra-low speed motor control).

The present disclosure proposes a new concept of a pseudo zero vector(alternatively this may be called a quasi zero vector, or a syntheticzero vector) to SVM to address the above-mentioned problems. With thenew SVM using pseudo zero vectors, one is able to provide low-cost,high-quality, more reliable, and unique motor control solutions (e.g.,sensorless FOC with single-shunt current sensing) to customers. The newSVM with pseudo zero vectors may also be used in three-phase powerinverter control for uninterruptible power supplies, renewable energy,and etc.

The space vector diagram (a regular hexagon) 120 and reference vectorapproximation 130 of the existing conventional SVM are shown in FIGS. 3and 4, respectively. {right arrow over (V)}₁ to {right arrow over (V)}₆are active vectors. {right arrow over (V)}₀ and {right arrow over (V)}₇do not generate any voltage difference in the inverter outputs and arethe only two zero vectors (or passive vectors) in existing SVM. Therevolving reference vector {right arrow over (V)}_(ref)=|V_(ref)|·e^(jθ)is approximated by two adjacent active vectors (e.g., {right arrow over(V)}₁, {right arrow over (V)}₂ in sector A) and one or both of theexisting zero vectors (e.g., {right arrow over (V)}₀ only). The plane ofthe space vector hexagon is dissected in six sectors from A to F and theangle θ of {right arrow over (V)}_(ref) is transformed into the relativeangle θ_(rel) in each sector. Using reference vector in sector A as anexample, the following portion shows the calculations of existing orconventional SVM.

Using volt-second balancing:

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{T_{0}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{T_{1}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{T_{2}}{T_{S}}{\overset{\rightarrow}{V}}_{2}}}} & (1) \\{T_{S} = {T_{0} + T_{1} + T_{2}}} & (2)\end{matrix}$

Solving the Equations (1) and (2), one obtains:

T ₁ =K sin(60°−θ_(rel))·T _(S)  (3)

T ₂ =K sin(θ_(rel))·T _(S)  (4)

Adding the Equations (3) and (4), one obtains:

T ₁ +T ₂ =K sin(60°+θ_(rel))·T _(S)  (5)

So the zero vector time is:

T ₀ =T _(S)−(T ₁ +T ₂)=[1−K sin(60°+θ_(rel))]·T _(S)  (6)

where:

T₀—Time of the zero vector(s) is/are applied. The zero vector(s) can be{right arrow over (V)}₀ [000], or {right arrow over (V)}₇ [111], or both

T₁—Time of the 1^(st) active vector (e.g., {right arrow over (V)}₁ insector A) is applied within one sampling period,

T₂—Time of the 2^(nd) active vector (e.g., {right arrow over (V)}₂ insector A) is applied within one sampling period,

K—

$K = {\sqrt{3} \cdot \frac{V_{ref}}{V_{D\; C}} \cdot {V_{ref}}}$

is the amplitude of {right arrow over (V)}_(ref), and V_(DC) is theinverter DC link voltage,

T_(S)—Sampling period, e.g., T_(S)=50 μs

As T₀≧0 (or T₁+T₂≦T_(S)) all the time, so K≦1. We have inverter DC linkvoltage utilization without over-modulation:

$\begin{matrix}{\eta = {\frac{V_{ref}}{V_{D\; C}} \leq \frac{1}{\sqrt{3}}}} & (7)\end{matrix}$

Plots of normalized time T₁ 140 and T₂ 150 of Equations (3) and (4) areshown in FIG. 5. It is obvious that either T₁ or T₂ is close or equal tozero at the border of each sector (e.g., near θ=0° or 60° in sector A),which is the root cause of the above-mentioned problem (1) for motorcontrol with SVM and single-shunt current sensing. There have beennumerous prior attempts to solve this problem, but each solution has itsdisadvantages.

For example, motor phase current construction from DC link current via asingle-shunt resistor is done by limiting T₁ and T₂ with a time T_(min)(which is PWM dead time+driver delay+ADC sampling time) for ADC tosample the correct current values. However, limiting T₁ and T₂ willgenerate a distorted voltage vector, and therefore result in high torqueripple, high vibration & acoustic noise, and even unstable motor controlwith high dynamic loads. A very fast ADC is required to optimize thesystem performance in such instances.

Another conventional solution is modifying the SVM switching pattern toa minimum measurement time window in order to allow two current samplesto be taken. This pattern modification could generate some currentripple; moreover, more CPU resources are needed to implement thealgorithm due to modification of patterns and correction of the samemodifications.

Another conventional solution employs use of asymmetrical PWM pulses(with two PWM pulses shifted to obtain enough time for current samplingwhile duty cycles for all the PWM pulses preserved) only partly solvesthe problem. It can be found that both T₁ and T₂ are close or equal tozero if K is very small or K=0, which causes the problem (2) mentionedabove. Using the asymmetrical PWM pulses just mentioned can only partlysolve this problem.

The present disclosure proposes a new concept of a pseudo zero vector toSVM, with which the approximation of the reference vector with more thantwo active vectors becomes relatively easy and straightforward. (Incontrast, existing SVM uses only two adjacent active vectors toapproximate the reference vector). The pseudo zero vectors shown inFIGS. 6A-6E complement the existing two zero vectors and expand the SVMtheory, giving more choice of zero vectors in the approximation of thereference vector.

A basic pseudo zero vector is either a combination of two active vectors160, 170, or 180 as shown in FIGS. 6A, 6B and 6C, or a combination ofthree active vectors 190 or 200 as shown in FIGS. 6D and 6E. The pseudozero vector time T_(z) shown in FIGS. 6A-6E can be time-variant,θ-angle-dependent, or constant, depending on the different applicationrequirements. These pseudo zero vectors have similar effects of existingzero vectors (i.e., they do not generate any voltage difference in theinverter outputs). Any combinations of the pseudo zero vectors also givethe same effects. The pseudo zero vectors can be used in similar ways asthe existing zero vectors are used (i.e., one, two, or a combination ofzero vectors being used in the approximation of a reference vector).

The advantages of the new concept of a pseudo zero vector according tothe present disclosure are that there are many more choices of “zerovectors” in the SVM approximation. The approximation of the referencevector with more than two active vectors becomes very easy andconvenient. Additionally, the corresponding calculations are similar tothose of the existing SVM, and thus are relatively simple and fast.

Two SVM examples according to the present disclosure are provided belowwith selective utilization of the pseudo zero vectors. Both new SVMexamples have non-zero time intervals for two single-shunt currentsamplings within any PWM cycle, and hence can easily solve theabove-mentioned problem (1). Further, and advantageously, new SVMExample #2 can completely solve problem (2) mentioned above.

In the new SVM examples, engineers can tune the pseudo zero vector timeT_(z) to obtain different current sampling intervals based on differentsystem requirements and hardware designs, so as to achieve the bestperformance of motor control with single-shunt current sensing.Particularly, as the long ADC sampling intervals can be obtained easilyby selecting longer pseudo zero vector time T_(z), it is also possibleto use a low-speed, common and low-cost operational amplifier (if any)for DC link current signal amplification to further lower the systemcost.

Table 1 summarizes the basic voltage space vectors for the SVM with thenew concept of a pseudo zero vector.

TABLE 1 Basic voltage space vectors of SVM with new concept of pseudozero vector Basic Voltage Space Vector Remark Active {right arrow over(V)}₁ [100] These are all the Vectors {right arrow over (V)}₂ [110]eight basic voltage {right arrow over (V)}₃ [010] space vectors of{right arrow over (V)}₄ [011] existing SVM. {right arrow over (V)}₅[001] {right arrow over (V)}₆ [101] Existing {right arrow over (V)}₀[000] Zero {right arrow over (V)}₇ [111] Vectors Pseudo Zero Vectors$\begin{matrix}{{\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{1}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{4}}} \\{{\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{2}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{5}}} \\{{\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{3}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{6}}} \\{{\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{1}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{3}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{5}}} \\{{\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{2}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{4}} + {\frac{T_{z}}{T_{S}}{\overset{->}{V}}_{6}}}\end{matrix}\quad$ New concept for SVM. T_(z) can be time-variant, θ-angle-dependent, or constant.

An element of the disclosure is the introduction of the new concept of apseudo zero vector to SVM. With the new pseudo zero vectors, there aremany more choices of zero vectors compared to the only two in existingor conventional SVM, which gives more flexibility for the approximationof the reference vector as well as the design of the SVM switchingsequences. The approximation of a reference vector with more than twoactive vectors becomes relatively easy and convenient. In addition, thecorresponding calculations are similar to that of existing SVM, andhence relatively simple and fast.

This section shows two examples of selective utilization of pseudo zerovectors in SVM to straightforwardly solve the single-shunt motor controlproblems that the existing SVM has difficulties in dealing witheffectively.

New SVM Example #1

Using sector A as an example as shown in FIGS. 7A and 7B, the referencevector {right arrow over (V)}_(ref) 210, 220 is approximated by twoadjacent active vectors, one pseudo zero vector, and one or both of theexisting zero vectors. Combining the time of the same active vectors(e.g:

$\frac{T_{2}^{\prime}}{T_{S}}{\overset{\rightarrow}{V}}_{2}\mspace{14mu} {and}\mspace{14mu} \frac{T_{z}}{T_{S}}{\overset{\rightarrow}{V}}_{2}$

in FIG. 7A), {right arrow over (V)}_(ref) is actually approximated bythree active vectors (e.g., {right arrow over (V)}₁, {right arrow over(V)}₂ and {right arrow over (V)}₄ in FIG. 7B and {right arrow over(V)}₁, {right arrow over (V)}₂ and {right arrow over (V)}₅ in FIG. 7A).This new SVM Example #1 is elaborated in greater detail below.

New SVM Example #2

Using sector A as an example as shown in FIG. 8, the reference vector{right arrow over (V)}_(ref) 230 is approximated by two adjacent activevectors, two pseudo zero vectors, and one or both of the existing zerovectors. Combining the time of the same active vectors (i.e.:

${\frac{T_{1}^{\prime}}{T_{S}}{\overset{\rightarrow}{V}}_{1}\mspace{14mu} {and}\mspace{14mu} \frac{T_{z}}{T_{S}}{\overset{\rightarrow}{V}}_{1}},{\frac{T_{2}^{\prime}}{T_{S}}{\overset{\rightarrow}{V}}_{2}\mspace{14mu} {and}\mspace{14mu} \frac{T_{z}}{T_{S}}{\overset{\rightarrow}{V}}_{2}}$

), {right arrow over (V)}_(ref) is actually approximated by four activevectors. The new SVM Example #2 is elaborated in greater detail below aswell.

Table 2 compares and summarizes the existing SVM and the new SVMexamples with pseudo zero vectors.

TABLE 2 Comparison of existing SVM and new SVM examples using pseudozero vectors Active {right arrow over (V)}_(ref) Angle Vectors For{right arrow over (V)}_(ref) θ Approximation (limit 0° ≦ θ < 360°) Note1 Sector Start End θ_(rel) 1^(st) 2^(nd) 3^(rd) 4^(th) Formulas ExistingSVM A B C D E F  0°  60° 120° 180° 240° 300°  60° 120° 180° 240° 300°360° θ-0° θ-60° θ-120° θ-180° θ-240° θ-300° {right arrow over (V)}₁{right arrow over (V)}₂ {right arrow over (V)}₃ {right arrow over (V)}₄{right arrow over (V)}₅ {right arrow over (V)}₆ {right arrow over (V)}₂{right arrow over (V)}₃ {right arrow over (V)}₄ {right arrow over (V)}₅{right arrow over (V)}₆ {right arrow over (V)}₁ — — — — — — — — — — — —T₁ = Ksin(60° − θ_(rel)) · T_(S) T₂ = Ksin(θ_(rel)) · T_(S) T₀ = T_(s) −(T₁ + T₂) $\begin{matrix}{{{where}\mspace{14mu} K} = {{\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}\mspace{14mu} {and}}} \\{\frac{V_{ref}}{V_{DC}} \leq \frac{1}{\sqrt{3}}}\end{matrix}\quad$ New SVM Example #1 A1   A2 B1 B2 C1 C2 D1 D2 E1 E2 F1F2  0°   Θ_(Tr)  60°  60° + Θ_(Tr) 120° 120° + Θ_(Tr) 180° 180° + Θ_(Tr)240° 240° + Θ_(Tr) 300° 300° + Θ_(Tr) Θ_(Tr) Note 2  60°  60° + Θ_(Tr)120° 120° + Θ_(Tr) 180° 180° + Θ_(Tr) 240° 240° + Θ_(Tr) 300° 300° +Θ_(Tr) 360° θ-0°   θ-0° θ-60° θ-60° θ-120° θ-120° θ-180° θ-180° θ-240°θ-240° θ-300° θ-300° {right arrow over (V)}₁   {right arrow over (V)}₁{right arrow over (V)}₂ {right arrow over (V)}₂ {right arrow over (V)}₃{right arrow over (V)}₃ {right arrow over (V)}₄ {right arrow over (V)}₄{right arrow over (V)}₅ {right arrow over (V)}₅ {right arrow over (V)}₆{right arrow over (V)}₆ {right arrow over (V)}₂   {right arrow over(V)}₂ {right arrow over (V)}₃ {right arrow over (V)}₃ {right arrow over(V)}₄ {right arrow over (V)}₄ {right arrow over (V)}₅ {right arrow over(V)}₅ {right arrow over (V)}₆ {right arrow over (V)}₆ {right arrow over(V)}₁ {right arrow over (V)}₁ {right arrow over (V)}₅   {right arrowover (V)}₄ {right arrow over (V)}₆ {right arrow over (V)}₅ {right arrowover (V)}₁ {right arrow over (V)}₆ {right arrow over (V)}₂ {right arrowover (V)}₁ {right arrow over (V)}₃ {right arrow over (V)}₂ {right arrowover (V)}₄ {right arrow over (V)}₃ —   — — — — — 1). For 0° ≦ θ_(rel) <Θ_(Tr): T₁ = Ksin(60° − θ_(rel)) · T_(S) T₂ = [Ksin(θ_(rel)) + λ] ·T_(S) 2). For Θ_(Tr) ≦ θ_(rel) < 60°: T₁ = [Ksin(60° − θ_(rel)) + λ] ·T_(S) T₂ = Ksin(θ_(rel)) · T_(S) For both conditions 1) & 2): T₃ = T_(z)= λT_(S) Note 3 T₀ = T_(s) − (T₁ + T₂ + T₃) $\begin{matrix}{{{{where}\mspace{14mu} K} = {\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}},{\lambda = \frac{T_{z}}{T_{S}}},{and}} \\{\frac{V_{ref}}{V_{DC}} \leq \frac{1 - {2\lambda}}{\sqrt{3}}}\end{matrix}\quad$ New SVM Example #2 A B C D E F  0°  60° 120° 180°240° 300°  60° 120° 180° 240° 300° 360° θ-0° θ-60° θ-120° θ-180° θ-240°θ-300° {right arrow over (V)}₁ {right arrow over (V)}₂ {right arrow over(V)}₃ {right arrow over (V)}₄ {right arrow over (V)}₅ {right arrow over(V)}₆ {right arrow over (V)}₂ {right arrow over (V)}₃ {right arrow over(V)}₄ {right arrow over (V)}₅ {right arrow over (V)}₆ {right arrow over(V)}₁ {right arrow over (V)}₄ {right arrow over (V)}₅ {right arrow over(V)}₆ {right arrow over (V)}₁ {right arrow over (V)}₂ {right arrow over(V)}₃ {right arrow over (V)}₅ {right arrow over (V)}₆ {right arrow over(V)}₁ {right arrow over (V)}₂ {right arrow over (V)}₃ {right arrow over(V)}₄ T₁ = [Ksin(60° − θ_(rel)) + λ] · T_(S) T₂ = [Ksin(θ_(rel)) + λ] ·T_(S) T₃ = T_(z) = λT_(S) T₄ = T_(z) = λT_(S) T₀ = T_(s) − (T₁ + T₂ +T₃ + T₄) $\begin{matrix}{{{{where}\mspace{14mu} K} = {\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}},{\lambda = \frac{T_{z}}{T_{S}}},{and}} \\{\frac{V_{ref}}{V_{DC}} \leq \frac{1 - {4\lambda}}{\sqrt{3}}}\end{matrix}\quad$ Note 1: The 3^(rd) and 4^(th) active vectors (if any)come from the pseudo zero vectors being used. Note 2: Θ_(Tr) is atransition angle for new sectors (e.g.: A1, A2, B1, B2, and etc), and 0°< Θ_(Tr) < 60°. Note 3: Pseudo zero vector time T_(z) = λT_(S) ≧T_(min), where T_(min) is PWM dead time + driver delay + ADC samplingtime.

New SVM Example #1 SVM with One Pseudo Zero Vector

As shown in FIGS. 7A and 7B, the reference vector in each existingsector (i.e., A, B, C, D, E, and F) can be approximated by two differentsets of active vectors. A transition angle Θ_(Tr) (0°<Θ_(Tr)<60°) isintroduced to get new sectors A1, A2, B1, B2, and so on as shown inTable 2. Therefore in FIG. 7A the reference vector 210 is in sector A1,and in FIG. 7B the reference vector 220 is in sector A2. At thetransition angles the reference vector approximation transits from oneset of active vectors to another set of active vectors for the new SVMs.Θ_(Tr) can be different in different existing sectors. For simplicity,we can choose the same value, e.g., Θ_(Tr)=30°, for all the sectors.

Calculations when 0°≦θ_(rel)<Θ_(Tr)

Using the reference vector 210 in sector A as shown in FIG. 7A as anexample, the following shows the calculations when 0°≦θ_(rel)<Θ_(Tr).Using volt-second balancing:

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{T_{0}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{T_{1}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{\overset{\overset{T_{2}}{}}{T_{2}^{\prime} + T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{2}} + {\frac{\overset{\overset{T_{3}}{}}{T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{5}}}} & (8) \\{T_{S} = {T_{0} + T_{1} + \underset{\underset{T_{2}}{}}{\left( {T_{2}^{\prime} + T_{z}} \right)} + \underset{\underset{T_{3}}{}}{T_{z}}}} & (9)\end{matrix}$

Choose T_(z) more than or equal to T_(min) (which is PWM deadtime+driver delay+ADC sampling time). For simplicity, select

T ₃ =T _(z) =λT _(S) ≧T _(min)  (10)

where: λ—A constant and

${\lambda = {\frac{T_{z}}{T_{S}}\left( {0 \leq \lambda \leq 1} \right)}},$

e.g., if T_(S)=50 μs and T_(min)=2 μs, we can select

$\lambda = {\frac{1}{25}.}$

Solve Equations (8) to (10) to get

T ₁ =K sin(60°−θ_(rel))·T _(S)

T ₂ =T ₂ ′+T _(z) =[K sin(θ_(rel))+λ]·T_(s)  (12)

T ₁ +T ₂ +T ₃ =[K sin(60°+θ_(rel))+2λ]·T _(S)  (13)

So the zero vector time is

T ₀ =T _(S)−(T ₁ +T ₂ +T ₃)=[(1−2λ)−K sin(60°+θ_(rel))]·T _(S)  (14)

where:

T₀—Time of existing zero vector(s) is applied. The zero vector(s) can be{right arrow over (V)}₀ [000], or {right arrow over (V)}₇ [111], or both

T_(z)—Time of pseudo zero vector is applied

T₁—Time of the 1^(st) active vector is applied within one samplingperiod

T₂—Time of the 2^(nd) active vector is applied within one samplingperiod

T₃—Time of the 3^(rd) active vector is applied within one samplingperiod, which is part of the pseudo zero vector being used

${K - K} = {\sqrt{3} \cdot {\frac{V_{ref}}{V_{DC}}.}}$

|V_(ref)| is the amplitude of {right arrow over (V)}_(ref), and V_(DC)is the inverter DC link voltage

T_(S)—Sampling period

As T₀≧0 all the time, from Equation (14) we find K≦1-2λ, so the inverterDC link voltage utilization without over-modulation is

$\begin{matrix}{\eta = {\frac{V_{ref}}{V_{DC}} \leq \frac{1 - {2\lambda}}{\sqrt{3}}}} & (15)\end{matrix}$

Calculations when Θ_(Tr)≦θ_(rel)<60°

Using the reference vector 220 in sector A as shown in FIG. 7B as anexample, the following shows the calculations when Θ_(Tr)≦θ_(rel)<60°.Using volt-second balancing:

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{T_{0}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{\overset{\overset{T_{1}}{}}{T_{1}^{\prime} + T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{T_{2}}{T_{S}}{\overset{\rightarrow}{V}}_{2}} + {\frac{\overset{\overset{T_{3}}{}}{T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{4}}}} & (16) \\{T_{S} = {T_{0} + \underset{\underset{T_{1}}{}}{\left( {T_{1}^{\prime} + T_{z}} \right)} + T_{2} + \underset{\underset{T_{3}}{}}{T_{z}}}} & (17)\end{matrix}$

Similarly, select T_(z)=λT_(S), i.e.,

T ₃ =λT _(s) ≧T _(min)  (18)

Solve Equations (16) and (17) to get

T ₁ =T ₁ ′+T _(z) =[K sin(60°−θ_(rel))+λ]·T_(S)  (19)

T ₂ =K sin(θ_(rel))·T _(S)  (20)

T ₁ +T ₂ +T ₃ =[K sin(60°+θ_(rel))+2λ]·T _(S)  (21)

So the zero vector time is

T ₀ =T _(S)−(T ₁ +T ₂ +T ₃)=[(1−2λ)−K sin(60°+θ_(rel))]·T _(S)  (22)

Likewise, it can be found that the inverter DC link voltage utilizationwithout over-modulation is the same as Equation (15). So the new SVMExample #1 has one maximum inverter DC link voltage utilization withoutover-modulation, which is

$\begin{matrix}{\eta_{\max} = \frac{1 - {2\lambda}}{\sqrt{3}}} & (23)\end{matrix}$

A plot of Equation (23) is shown in FIG. 9, which is the maximuminverter DC link voltage 240 utilization versus λ for Example 1. Whenλ=0, the new SVM becomes the existing SVM and

$\eta \leq {\frac{1}{\sqrt{3}}.}$

Plots of normalized time T₁ 250, T₂ 260, and T₃ 270 for the new SVMExample #1 are shown in FIG. 10 with Θ_(Tr)=30° for all the sectors. Itcan be found that T₁, T₂ and T₃ are all non-zero (except when K is verysmall or K=0). So the new SVM Example #1 can easily solve the problem(1) mentioned previously. Using single-shunt current sensing, at anytime it is a good choice to measure inverter DC link current during twotime intervals T₁ and T₂.

New SVM Example #2 SVM with Two Pseudo Zero Vectors

Using the reference vector 230 in sector A as shown in FIG. 8 as anexample, the following shows the calculations. Using volt-secondbalancing:

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{T_{0}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{\overset{\overset{T_{1}}{}}{T_{1}^{\prime} + T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{\overset{\overset{T_{2}}{}}{T_{2}^{\prime} + T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{2}} + {\frac{\overset{\overset{T_{3}}{}}{T_{z}}}{T_{S}}{\overset{\rightarrow}{V}}_{4}} + {\frac{\overset{\overset{T_{4}}{}}{T_{z}}}{T_{S}}\overset{\rightarrow}{V_{5}}}}} & (24) \\{T_{S} = {T_{0} + \underset{\underset{T_{1}}{}}{\left( {T_{1}^{\prime} + T_{z}} \right)} + \underset{\underset{T_{2}}{}}{\left( {T_{2}^{\prime} + T_{z}} \right)} + \underset{\underset{T_{3} + T_{4}}{}}{2T_{z}}}} & (25)\end{matrix}$

Similarly, select T_(z)=λT_(S), i.e.,

T ₃ =T ₄ =λT _(S) ≧T _(min)  (26)

Solve Equations (24) to (26) to get

T ₁ =T ₁ ′+T _(z) =[K sin(60°−θ_(rel))+λ]·T_(S)  (27)

T ₂ =T ₂ ′+T _(z) =[K sin(θ_(rel))+λ]·T_(S)  (28)

T ₁ +T ₂ +T ₃ +T ₄ =[K sin(60°+θ_(rel))+4λ]·T _(S)  (29)

So the zero vector time is

T ₀ =T _(S)−(T ₁ +T ₂ +T ₃ +T ₄)=[(1−4λ)−K sin(60°+θ_(rel))]·T_(S)  (30)

where:

T₀—Time of existing zero vector(s) is applied. The zero vector(s) can be{right arrow over (V)}₀ [000], or {right arrow over (V)}₇ [111], or both

T_(z)—Time of pseudo zero vectors are applied

T₁—Time of the 1^(st) active vector is applied within one samplingperiod

T₂—Time of the 2^(nd) active vector is applied within one samplingperiod

T₃, T₄—Time of the 3^(rd) and 4^(th) active vectors are applied withinone sampling period, which are part of the pseudo zero vectors beingused

K—

$K = {\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}} \cdot {V_{ref}}}$

is the amplitude of {right arrow over (V)}_(ref), and V_(DC) is theinverter DC link voltage

T_(S)—Sampling period

As T₀≧0 all the time, from Equation (30) we find K≦1-4λ, so the inverterDC link voltage utilization without over-modulation is

$\begin{matrix}{\eta = {\frac{V_{ref}}{V_{DC}} \leq \frac{1 - {4\lambda}}{\sqrt{3}}}} & (31)\end{matrix}$

So the maximum inverter DC link voltage utilization withoutover-modulation is

$\begin{matrix}{\eta_{\max}^{\prime} = \frac{1 - {4\lambda}}{\sqrt{3}}} & (32)\end{matrix}$

Plot of Equation (32) is shown in FIG. 11 at 280, which shows themaximum inverter DC link voltage utilization versus A for new Example 2.When λ=0, the new SVM becomes the existing SVM and

$\eta \leq {\frac{1}{\sqrt{3}}.}$

Plots of normalized time T₁ 290, T₂ 300, T₃ and T₄ 310 for new SVMExample #2 are shown in FIG. 12. It can be found that both T₁ and T₂ arelonger than T_(min) in all conditions (as long as λT_(S)≧T_(min)), evenwhen K=0 (i.e.: |V_(ref)|=0). So the New SVM Example #2 not only cansolve the problem (1), but also can completely solve the problem (2)mentioned above. Using single-shunt current sensing, at any time it is agood choice to measure inverter DC link current during two timeintervals T₁ and T₂.

Usage of new SVM in motor control: The connections of SVM in a motorcontrol are shown in FIGS. 13A and 13B. The input to the new SVM can bethe polar coordinates (i.e., radial coordinate |V_(ref)| and angularcoordinate θ) of the reference vector {right arrow over (V)}_(ref) asshown in FIG. 13A, which has been discussed above. The inputs to the SVMcan also be the Cartesian coordinates (V_(α), V_(β)) of the referencevector {right arrow over (V)}_(ref) in the α-β Cartesian coordinatesystem, as shown in FIG. 13B. The coordinate systems in the SVM spacevector hexagon are shown in FIG. 14. The Polar-to-Cartesian Transformis:

V _(α) =|V _(ref)|cos(θ)  (33)

V _(β) =|V _(ref)|sin(θ)  (34)

With Equations (33) and (34), all the formulas listed in Table 2 can betransferred to format with inputs of V_(α) and V_(β). For example, thetime calculations of New SVM Example #1 in sector A1 become

$\begin{matrix}{T_{1} = {\frac{\sqrt{3}T_{S}}{2V_{DC}} \cdot \left( {{\sqrt{3}V_{\alpha}} - V_{\beta}} \right)}} & (35) \\{T_{2} = {{\frac{\sqrt{3}T_{S}}{V_{DC}} \cdot V_{\beta}} + {\lambda \; T_{S}}}} & (36) \\\begin{matrix}{T_{3} = T_{z}} \\{= {\lambda \; T_{S}}}\end{matrix} & (37) \\{T_{0} = {T_{S} - \left( {T_{1} + T_{2} + T_{3}} \right)}} & (38)\end{matrix}$

FIG. 13A shows a control system 320, for example, a motor controlsystem. The control system 320 includes a space vector modulator (SVM)330 according to the present disclosure that utilizes pseudo zerovectors. The SVM 330 receives a reference signal or reference samplesand synthesizes one or more reference vectors based thereon, wherein atleast one of the reference vectors employ one or more pseudo zerovectors as described herein. Based on the synthesized referencevector(s), the SVM modulator 330 outputs timing signals 340 to a PWMunit 350 that receives the timing signals 340 and generates PWM controlsignals 360. The PWM control signals 360 are provided to a three-phaseinverter circuit 370 which generates output signals u, v, and w to drivea load 380 such as a three-phase motor. FIG. 13B, as highlighted above,is similar to FIG. 13A, but illustrates receiving an input referencesignal in Cartesian coordinates rather than polar coordinates, butgenerally operates in the same manner as that described above.

Inverter with single-shunt current sensing: The connection of athree-phase two-level voltage source inverter and a motor are shown inFIG. 15 at 400. The six switching devices of the inverter 400, whichcould be MOSFET, IGBT or similar parts, are controlled bymicrocontroller PWM signals. As illustrated, the inverter comprises afirst pair of series-connected switches 410, a second pair ofseries-connected switches 420, and a third pair of series-connectedswitches 430. Each of the series-connected pairs 410, 420, and 430 areconnected at a node that forms an output u, v, w that connects to arespective phase of the load 440. Each of the series-connected pairs410, 420, 430 also couple together at a terminal 450 that couples to afirst terminal of a shunt resistor 460 that has a second terminalconnected to a reference potential 470. An amplifier 480 has inputterminals coupled to the first and second terminals of the shuntresistor 460, respectively, wherein an output of the amplifier 480reflects a current conducting through the shunt resistor 460.

The motor windings can be wired in a star (as shown) or a deltaconfiguration. SVM is used to control the PWM to create three-phasesinusoidal waveforms to the motor windings. The shunt resistor R_(shunt)460 is inserted into the inverter DC link to sense the DC link current.If needed, the amplifier 480 is used to amplify the resistor voltagedrop which is proportional to the DC link current. Note that a Hallsensor, a current transformer, or other current sensors can replace theshunt resistor to sense the DC link current.

Compared to dual-shunt and triple-shunt current sensing, single-shuntcurrent sensing has the following important advantages:

1) Cost reduction as a result of only one current sensor, one amplifier(if any), and one ADC channel are used. In contrast, dual-shunt currentsensing and triple-shunt current sensing need multiple current sensors,amplifiers (if any) and ADC channels.2) No need to calibrate amplifier gains and offsets (which may due tocomponent tolerance, fluctuating temperature, aging, and etc) since thesame current sensing circuit and ADC channel are used for all thecurrent measurements of motor phases.3) Simpler and easier electronic schematics and PCB design.Switching sequence design: There are a lot of switching sequencecombinations for the new SVMs, depending on different sequencings ofactive/zero vectors, splitting of the duty cycles of the vectors, andchoice of existing zero vectors (i.e., to choose zero vector {rightarrow over (V)}₀ [000], or {right arrow over (V)}₇[111], or both). It isdifficult to list all the switching sequences here. This section onlygives some examples of the switching sequences, which can be easilyimplemented using Infineon microcontrollers or other typemicrocontrollers. FIGS. 16A and 16B show examples of 5-segment switchingsequences 500, 510 for new SVM Example #1. FIGS. 17A and 17B showexamples of 5-segment switching sequences 520, 530 for new SVM Example#2, FIGS. 18A and 18B show examples of 6-segment switching sequences540, 550, and FIGS. 19A and 19B show examples of 7-segment switchingsequences 560, 570.

Current reconstruction: Two/three motor phase currents can bereconstructed by using single-shunt current sensing. In each PWM cycle,the inverter DC link current is measured at least twice during twodifferent active vector segments to get two motor phase currents. TheADC samplings are normally triggered near the center of the activevector segments to avoid current transitions. Table 3 shows the inverterDC link current of different PWM segments. As an example, FIG. 20 showsthe DC link current I_(DClink) 580 corresponding to the switchingsequences 540 shown earlier in FIG. 18A. Two phase currents can bemeasured at two PWM active vector segments which are more than or equalto T_(min), e.g.: I_(DClink)=−I_(W) during T₂ and I_(DClink)=I_(U)during T₁ in FIG. 20 since T₂≧T_(min) and T₁≧T_(min). With two phasecurrents, the third motor phase current can be calculated easily becauseI_(U)+I_(V)+I_(W)=0.

TABLE 3 Inverter DC link current of different PWM segments Inverter DClink current PWM Segment I_(DClink) ^(Note 1) Remark Active {right arrowover (V)}₁ [100] I_(U) Take current Vectors {right arrow over (V)}₂[110] −I_(W) sample for {right arrow over (V)}₃ [010] I_(V) motor phase{right arrow over (V)}₄ [011] −I_(U) current {right arrow over (V)}₅[001] I_(W) {right arrow over (V)}₆ [101] −I_(V) Zero {right arrow over(V)}₀ [000] 0 If needed, can Vectors {right arrow over (V)}₇ [111] 0 beused for channel offset calibration ^(Note 1)I_(U), I_(V) and I_(W) arethe currents of motor phases U, V and W, respectively.

Using a reference vector {right arrow over (V)}_(ref) in sector A as anexample, FIG. 21 shows an alternative approximation of the referencevector 590 with one pseudo zero vector in accordance with anotherembodiment of the disclosure. Clearly, calculations for T₁ and T₂ arethe same as those for the existing SVM, and the reference vector 590 isactually approximated by four active vectors. It is another example ofselective utilization of a pseudo zero vector to easily solve theproblems mentioned above.

As highlighted above, SVM is regularly employed for industry andautomotive motor control applications, and used in the sinusoidalcommutation control (such as V/f, FOC, and DTC) of PMSM and ACIM togenerate sine waveforms from three-phase inverters. Sinusoidalcommutation motor control with a single-shunt current sensing resistorinserted in the inverter DC link is a desired solution when compared todual-shunt and triple-shunt current sensing techniques, owing to itsimportant advantages such as low cost, simplicity and etc. However, twocurrent samples within one PWM cycle are needed for correct motor phasecurrent reconstruction with single-shunt current sensing. But withexisting SVM, the accurate current construction is difficult when thereference voltage space vector is crossing a sector border, as in thatsituation only one current sample can be measured. It is a problem formost of the normal speed motor control with SVM and single-shunt currentsensing.

The enhanced SVM proposed in accordance with one embodiment of thedisclosure can solve the above-mentioned problem. With the new SVMtechnology, one can offer low-cost, high-quality, more reliable, andunique motor control solutions (e.g., sensorless FOC with single-shuntcurrent sensing) to customers. The enhanced SVM may also be used inthree-phase power inverter control for uninterruptible power supplies,renewable energy, and etc.

To solve the problems highlighted above associated with conventionalSVM, the present disclosure according to the present embodimentintroduces innovative approximations of the reference vector withdifferent active vectors, instead of two adjacent active vectors inexisting SVM. New approximations of the enhanced SVM are shown in FIGS.22A-22B. One portion (i.e., m{right arrow over (V)}_(ref) with 0≦m≦1) ofthe reference vectors 600, 610 is approximated by two adjacent activevectors just like the existing SVM, and the remaining portion(1−m){right arrow over (V)}_(ref) is approximated by two non-adjacentand 120°-separated active vectors. The enhanced SVM is elaborated below.One special case of the enhanced SVM is when m=1, the entire referencevector {right arrow over (V)}_(ref) is approximated by two adjacentactive vectors in each sector, and the enhanced SVM becomes the existingSVM as shown in FIG. 4. Another special case of the enhanced SVM is whenm=0, the entire reference vector {right arrow over (V)}_(ref) isapproximated by two non-adjacent and 120°-separated active vectors ineach sector. So the approximations 600, 610 in FIGS. 22A and 22B becomeapproximations 620, 630 in FIGS. 23A and 23B, respectively. The enhancedSVM becomes another new SVM (which is called “Enhanced SVM at m=0” inthis disclosure) and which is described in detail below.

Table 4 compares and summarizes the existing SVM and proposed new SVMs.

TABLE 4 Comparison of existing SVM and proposed enhanced SVMs {rightarrow over (V)}_(ref) Angle Active θ Vectors For {right arrow over(V)}_(ref) (limit 0° ≦ θ < 360°) Approximation Sector Start End θ_(rel)1^(st) 2^(nd) 3^(rd) Formulas Existing SVM (A special case of EnhancedSVM at m = 1) A B C D E F  0°  60° 120° 180° 240° 300°  60° 120° 180°240° 300° 360° θ-0° θ-60° θ-120° θ-180° θ-240° θ-300° {right arrow over(V)}₁ {right arrow over (V)}₂ {right arrow over (V)}₃ {right arrow over(V)}₄ {right arrow over (V)}₅ {right arrow over (V)}₆ {right arrow over(V)}₂ {right arrow over (V)}₃ {right arrow over (V)}₄ {right arrow over(V)}₅ {right arrow over (V)}₆ {right arrow over (V)}₁ — — — — — — T₁ =Ksin(60° − θ_(rel)) · T_(S) T₂ = Ksin(θ_(rel)) · T_(S) T₀ = T_(s) −(T₁ + T₂)${{where}\mspace{14mu} K} = {{{\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}\mspace{14mu} {and}\mspace{14mu} \frac{V_{ref}}{V_{DC}}} \leq {\frac{1}{\sqrt{3}}\quad}}$Enhanced SVM (0 ≦ m ≦ 1) AB   BC CD DE EF FA Θ_(Tr) Note 1  60° + Θ_(Tr)120° + Θ_(Tr) 180° + Θ_(Tr) 240° + Θ_(Tr) 300° + Θ_(Tr)  60° + Θ_(Tr)  120° + Θ_(Tr) 180° + Θ_(Tr) 240° + Θ_(Tr) 300° + Θ_(Tr) Θ_(Tr) θ-0°  θ-60° θ-120° θ-180° θ-240° θ-300° {right arrow over (V)}₁   {right arrowover (V)}₂ {right arrow over (V)}₃ {right arrow over (V)}₄ {right arrowover (V)}₅ {right arrow over (V)}₆ {right arrow over (V)}₂   {rightarrow over (V)}₃ {right arrow over (V)}₄ {right arrow over (V)}₅ {rightarrow over (V)}₆ {right arrow over (V)}₁ {right arrow over (V)}₃  {right arrow over (V)}₄ {right arrow over (V)}₅ {right arrow over (V)}₆{right arrow over (V)}₁ {right arrow over (V)}₂ 1). For Θ_(Tr) ≦ θ_(rel)< 60°: T₁ = {square root over (1 − m(1 − m))} · K · sin(Θ₁ − θ_(rel)) ·T_(S) Note 2 T₂ = mKsin(θ_(rel)) · T_(S) T₃ = (1 − m)Ksin(θ_(rel)) ·T_(S) 2). For 60° ≦ θ_(rel) < 60° + Θ_(Tr): T₁ = (1 − m)Ksin(120° −θ_(rel)) · T_(S) T₂ = mKsin(120° − θ_(rel)) · T_(S) T₃ = {square rootover (1 − m(1 − m))} · K · sin(θ_(rel) − Θ₃) · T_(S) Note 3 For bothconditions 1) and 2): T₀ = T_(s) − (T₁ + T₂ + T₃)${{{where}\mspace{14mu} K} = {\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}},{{{and}\mspace{14mu} \frac{V_{ref}}{V_{DC}}} \leq {\frac{1}{\sqrt{9 - {3{m\left( {3 - m} \right)}}}}\quad}}$Enhanced SVM at m = 0 (A special case of Enhanced SVM) AB BC CD DE EF FAΘ_(Tr)  60° + Θ_(Tr) 120° + Θ_(Tr) 180° + Θ_(Tr) 240° + Θ_(Tr) 300° +Θ_(Tr)  60° + Θ_(Tr) 120° + Θ_(Tr) 180° + Θ_(Tr) 240° + Θ_(Tr) 300° +Θ_(Tr) Θ_(Tr) θ-0° θ-60° θ-120° θ-180° θ-240° θ-300° {right arrow over(V)}₁ {right arrow over (V)}₂ {right arrow over (V)}₃ {right arrow over(V)}₄ {right arrow over (V)}₅ {right arrow over (V)}₆ — — — — — — {rightarrow over (V)}₃ {right arrow over (V)}₄ {right arrow over (V)}₅ {rightarrow over (V)}₆ {right arrow over (V)}₁ {right arrow over (V)}₂ T₁ =Ksin(120° − θ_(rel)) · T_(S) T₃ = Ksin(θ_(rel)) · T_(S) T₀ = T_(s) −(T₁ + T₃)${{where}\mspace{14mu} K} = {{{\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}}}\mspace{14mu} {and}\mspace{14mu} \frac{V_{ref}}{V_{DC}}} \leq \frac{1}{3}}$Note 1: Θ_(Tr) is a transition angle for new sectors (i.e., AB, BC CD,DE, EF, and FA), and 0° < Θ_(Tr) < 60°. Note 2:$\Theta_{1} = {{{\arctan \mspace{11mu} \left( \frac{\sqrt{3}}{{2m} - 1} \right)} + {k\; \pi \mspace{14mu} {where}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {{integer}.\mspace{14mu} {Select}}\mspace{14mu} k\mspace{14mu} {so}\mspace{14mu} {that}\mspace{14mu} 60{^\circ}}} \leq \Theta_{1} \leq {120{^\circ}\mspace{14mu} {for}\mspace{14mu} 0} \leq m \leq 1.}$Note 3:$\Theta_{3} = {{{\arctan \mspace{11mu} \left( \frac{\sqrt{3}m}{2 - m} \right)} + {k\; \pi \mspace{14mu} {where}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {{integer}.\mspace{14mu} {Select}}\mspace{14mu} k\mspace{14mu} {so}\mspace{14mu} {that}\mspace{14mu} 0{^\circ}}} \leq \Theta_{3} \leq {60{^\circ}\mspace{14mu} {for}\mspace{14mu} 0} \leq m \leq {1.\quad}}$

As highlighted previously, enhanced SVM has advantages over conventionalSVM techniques. For example, enhanced SVM is well suited for three-phasemotor control with single-shunt current sensing, so it can fully use theadvantages of a single-shunt current sensing technique as elaborated ingreater detail below. Another advantage of the enhanced SVM is thatcustomers can tune the factor m to obtain different current samplingintervals based on different system requirements and hardware designs,so as to achieve the best performance of motor control with single-shuntcurrent sensing. As three adjacent active vectors are used for theapproximation in the enhanced SVM, if necessary, it is possible to takethree ADC samplings of the inverter DC link current within one PWM cycleto get three motor phase currents directly (which will be discussed ingreater detail below). It will be useful for the application cases thatthe sum of three motor winding currents is not zero but still usesingle-shunt current sensing. It is also possible to take only two ADCsamplings of the interested motor phase current (e.g., I_(U) and I_(V)only) directly within any PWM cycle.

The enhanced SVM at m=0 is also well suited for motor control withsingle-shunt current sensing. It has long current sampling timeintervals within every PWM cycle, so it is possible to use a low-speed,common and low-cost operational amplifier for current signalamplification to further lower the system cost. The enhanced SVM at m=0has a lower DC link bus voltage utilization. It is not a problem forapplications with high DC link voltage, e.g., low-cost PMSM ceiling fandrive with very high DC link voltage (up to 400V DC due to the use ofpower factor correction).

Enhanced SVM: Using the reference vector in sector A as an example asshown in FIGS. 22A and 22B, the reference vector in each existing sector(i.e., A, B, C, D, E, or F) can be approximated by two different sets ofactive vectors. A transition angle Θ_(Tr) (0°<Θ_(Tr)<60°) is introducedto get new combined sectors AB, BC CD, DE, EF, and FA as shown inTable 1. At the transition angles the reference vector approximationtransits from one set of active vectors to another set of active vectorsfor the new SVMs. Θ_(Tr) can be different in different existing sectors.For simplicity, we can choose the same value, e.g., Θ_(Tr)=30°, for allthe sectors.

Calculations when Θ_(Tr)≦θ_(rel)<60°: Using reference vector in sector Aas shown in FIG. 22A as an example, the following shows the calculationswhen Θ_(Tr)≦θ_(rel)<60°. Using volt-second balancing:

$\begin{matrix}{{m{\overset{\rightarrow}{V}}_{ref}} = {{\frac{T_{0}^{\prime}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{T_{1}^{\prime}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{T_{2}}{T_{S}}{\overset{\rightarrow}{V}}_{2}}}} & (39) \\{{\left( {1 - m} \right){\overset{\rightarrow}{V}}_{ref}} = {{\frac{T_{0}^{''}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{T_{1}^{''}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{T_{3}}{T_{S}}{\overset{\rightarrow}{V}}_{3}}}} & (40)\end{matrix}$

Add both sides of Equations (39) and (40),

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{\overset{\overset{T_{0}}{}}{T_{0}^{\prime} + T_{0}^{''}}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{\overset{\overset{T_{1}}{}}{T_{1}^{\prime} + T_{1}^{''}}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{T_{2}}{T_{S}}{\overset{\rightarrow}{V}}_{2}} + {\frac{T_{3}}{T_{S}}{\overset{\rightarrow}{V}}_{3}}}} & (41) \\{T_{S} = {\underset{\underset{T_{0}}{}}{\left( {T_{0}^{\prime} + T_{0}^{''}} \right)} + \underset{\underset{T_{1}}{}}{\left( {T_{1}^{\prime} + T_{1}^{''}} \right)} + T_{2} + T_{3}}} & (42)\end{matrix}$

Solve Equations (39) and (40) to get

T ₁ ′=mK sin(60°−θ_(rel))·T _(S)  (43)

T ₁″=(1−m)K sin(120°−θ_(rel))·T _(S)  (44)

T ₂ =mK sin(θ_(rel))·T _(S)  (45)

T ₃=(1−m)K sin(θ_(rel))·T _(S)  (46)

where:

T₀—Time of zero vector(s) is applied. The zero vector(s) can be {rightarrow over (V)}₀ [000], or {right arrow over (V)}₇[111], or both

T₁—Time of the 1^(st) active vector is applied within one samplingperiod

T₂—Time of the 2^(nd) active vector is applied within one samplingperiod

T₃—Time of the 3^(rd) active vector is applied within one samplingperiod

K—

$K = {\sqrt{3} \cdot \frac{V_{ref}}{V_{DC}} \cdot {V_{ref}}}$

is the amplitude of {right arrow over (V)}_(ref), and V_(DC) is theinverter DC link voltage

T_(S)—Sampling period

Add both sides of Equations (43) and (44), it can be found that

T ₁ =T ₁ ′+T ₁″=√{square root over (1−m(1−m))}·K sin(Θ₁−θ_(rel))·T_(S)  (47)

where Θ₁ is an angle depending on the factor m only, and

$\begin{matrix}{\Theta_{1} = {{\arctan\left( \frac{\sqrt{3}}{{2m} - 1} \right)} + {k\; \pi}}} & (48)\end{matrix}$

where k is an integer and k=0, ±1, ±2, ±3, or . . . . Select k so that60°≦Θ₁≦120° for 0≦m≦1, e.g.: Θ₁=120° when m=0.Add both sides of Equations (45), (46) and (47) to get

T ₁ +T ₂ +T ₃=√{square root over (3−m(3−m))}·K sin(Θ₂+θ_(rel))·T_(S)  (49)

where: Θ₂—An angle depending on m only, and

${\Theta_{2} = {\arctan\left( \frac{\sqrt{3}}{3 - {2m}} \right)}},$

e.g.: Θ₂=30° when m=0. The zero vector time is

$\begin{matrix}\begin{matrix}{T_{0} = {{T_{0}^{\prime} + T_{0}^{''}} = {T_{S} - \left( {T_{1} + T_{2} + T_{3}} \right)}}} \\{= {\left\lbrack {1 - {{\sqrt{3 - \left( {3 - m} \right)} \cdot K}\; {\sin \left( {\Theta_{2} + \theta_{rel}} \right)}}} \right\rbrack \cdot T_{S}}}\end{matrix} & (50)\end{matrix}$

As T₀≧0 (or T₁+T₂+T₃≧T_(S)) all the time, so √{square root over(3−m(3−m))}·K≦1, so the inverter DC link voltage utilization withoutover-modulation is

$\begin{matrix}{\eta = {\frac{V_{ref}}{V_{D\; C}} \leq \frac{1}{\sqrt{9 - {3{m\left( {3 - m} \right)}}}}}} & (51)\end{matrix}$

Calculations when 60°≦θ_(rel)<60°±Θ_(Tr): Using reference vector insector A as an example as shown in FIG. 22B, the following show theslightly different calculations when 60°≦θ_(rel)<60°+Θ_(Tr). Similarlywe have

$\begin{matrix}{{\overset{\rightarrow}{V}}_{ref} = {{\frac{T_{0}}{T_{S}}{\overset{\rightarrow}{V}}_{0}} + {\frac{T_{1}}{T_{S}}{\overset{\rightarrow}{V}}_{6}} + {\frac{T_{2}}{T_{S}}{\overset{\rightarrow}{V}}_{1}} + {\frac{\overset{\overset{T_{3\;}}{}}{T_{3}^{\prime} + T_{3}^{''}}}{T_{S}}{\overset{\rightarrow}{V}}_{2}}}} & (52) \\{T_{S} = {T_{0} + T_{1} + T_{2} + \underset{\underset{T_{3}}{}}{\left( {T_{3}^{\prime} + T_{3}^{''}} \right)}}} & (53)\end{matrix}$

Solve Equations (52) and (53), we have

T ₁=(1−m)K sin(120°−θ_(rel))·T _(S)  (54)

T ₂ =mK sin(120°−θ_(rel))·T _(S)  (55)

T ₃ =T ₃ ′+T ₃″=√{square root over (1−m(1−m))}·K sin(θ_(rel)−Θ₃)·T_(S)  (56)

where: Θ₃—An angle depending on the factor m only, and

$\Theta_{3} = {{\arctan\left( \frac{\sqrt{3}m}{2 - m} \right)} + {k\; {\pi.}}}$

k is an integer and k=0, ±1, ±2, ±3, or . . . . Select k so that0°≦Θ₃≦60° for 0≦m≦1, e.g.: Θ₃=0° when m=0. The zero vector time is

$\begin{matrix}{T_{0} = {{T_{S} - T_{1} - T_{2} - T_{3}} = {\left\lbrack {1 - {{\sqrt{3 - {m\left( {3 - m} \right)}} \cdot K}\; {\sin \left( {\Theta_{4} + \theta_{rel}} \right)}}} \right\rbrack \cdot T_{S}}}} & (57)\end{matrix}$

where: Θ₄—An angle depending on m only, and

${\Theta_{4} = {\arctan\left\lbrack \frac{\sqrt{3}\left( {1 - m} \right)}{3 - m} \right\rbrack}},$

e.g.: Θ₄=30° when m=0. Likewise, it can be found that the inverter DClink voltage utilization without over-modulation is the same as Equation(51). So the enhanced SVM has one maximum inverter DC link voltageutilization without over-modulation, which is

$\begin{matrix}{\eta_{m\; {ax}} = \frac{1}{\sqrt{9 - {3{m\left( {3 - m} \right)}}}}} & (58)\end{matrix}$

Plot of Equation (58) is shown in FIG. 24 at 640. When m=1, the enhancedSVM becomes the existing SVM and

${\eta \leq \frac{1}{\sqrt{3}}},$

which has been stated in earlier Equation (7); when m=0, it becomes thespecial case of the enhanced SVM at m=0 and

$\eta \leq \frac{1}{3}$

(to be discussed in greater detail below).

Plots of normalized time T₁ 650, T₂ 660, and T₃ 670 for the enhanced SVMare shown in FIGS. 25A and 25B with Θ_(Tr)=30° for all the sectors, withm=0.8 and 0.2 as examples, respectively. It is obvious that T₁, T₂ andT₃ are all non-zero. Using single-shunt current sensing, at any time itis a good choice to measure inverter DC link current during two timeintervals which is longer than the third time (e.g., T₂ and T₃ when0°≦θ<30° as shown in FIG. 25A, T₁ and T₃ for all θ as shown in FIG.25B). At Θ_(Tr)=30°, it can be found that the minimum current samplingtime, which is limited by T₁, T₂ or T₃, is

$\begin{matrix}{{T_{minimum} = {\frac{\sqrt{3}\left( {1 - m} \right)}{2}{{KT}_{S}\left( {0.5 \leq m \leq 1} \right)}}}{or}} & (59) \\{T_{minimum} = {\frac{1 - m}{2}{{KT}_{S}\left( {0 \leq m < 0.5} \right)}}} & (60)\end{matrix}$

A user can choose the value of m based on the required maximum DC linkvoltage utilization, and the minimum time needed for the currentsampling (i.e., make sure T_(minimum)≧T_(min), where T_(min) is PWM deadtime+driver delay+ADC sampling time).

Enhanced SVM at m=0: Similarly, the calculations of the enhanced SVM atm=0 are shown below:

T ₁ =K sin(120°−θ_(rel))·T _(S)  (61)

T ₃ =K sin(θ_(rel))·T _(S)  (62)

T ₁ +T ₃=√{square root over (3)}·K sin(30°+θ_(rel))·T _(S)  (63)

T ₀ =T _(S)−(T ₁ +T ₃)=[1−√{square root over (3)}·K sin(30°+θ_(rel))]·T_(S)  (64)

Note that Equations (61) to (64) work for both FIGS. 23A and 23B. Theinverter DC link voltage utilization without over-modulation becomes

$\begin{matrix}{\eta = {\frac{V_{ref}}{V_{D\; C}} \leq \frac{1}{3}}} & (65)\end{matrix}$

Plot of normalized time T₁ 680 and T₃ 690 with transition angleΘ_(Tr)=30° for all the sectors is shown in FIG. 26. It is obvious thatboth T₁ and T₃ are non-zero. With Θ_(Tr)=30° the shortest time for thecurrent ADC sampling is

$\begin{matrix}{T_{minimum}^{\prime} = {\frac{1}{2} \cdot {KT}_{S}}} & (66)\end{matrix}$

One advantageous element of the disclosure according to this embodimentis that instead of two adjacent active vectors being employed tosynthesize a reference vector as in existing SVM, the enhanced SVM usesthree adjacent active vectors or two non-adjacent active vectors for theapproximation of reference vector {right arrow over (V)}_(ref). In thenew enhanced SVMs, non-zero intervals can be achieved for multiplecurrent samplings within one PWM cycle, and the reconstruction of phasecurrents with single-shunt current sensing can be easily done withoutintroducing distortion to the resulted motor phase current.

Usage of new SVM in motor control: The connections of SVM in a motorcontrol system 700 are shown in FIGS. 27A and 27B. FIG. 27A shows aportion of a control system 700, for example, a motor control system.The control system 700 includes a space vector modulator (SVM) 710according to the present disclosure that utilizes the enhanced SVM usingthree adjacent active vectors or two non-adjacent active vectors forsynthesizing a reference vector. The enhanced SVM 710 receives areference signal or reference samples and synthesizes one or morereference vectors based thereon, wherein at least one of the referencevectors employ either three adjacent active vectors or two non-adjacentactive vectors as described herein. Based on the synthesized referencevector(s), the SVM modulator 710 outputs timing signals 720 to a PWMunit 730 that receives the timing signals 720 and generates PWM controlsignals 740. The PWM control signals 740 are provided to a three-phaseinverter circuit 750 which generates output signals u, v, and w to drivea load 760 such as a three-phase motor.

The input to the new enhanced SVM can be the polar coordinates (i.e.,radial coordinate |V_(ref)| and angular coordinate θ) of the referencevector {right arrow over (V)}_(ref) as shown in FIG. 27A, which has beendiscussed above. The inputs to the SVM can also be the Cartesiancoordinates (V_(α), V_(β)) of the reference vector {right arrow over(V)}_(ref) in the α-β Cartesian coordinate system, as shown in FIG. 27B.

The coordinate systems in the SVM space vector hexagon are shown in FIG.28 at 770. The Polar-to-Cartesian Transform is:

V _(α) =|V _(ref)|cos(θ)  (67)

V _(β) =|V _(ref)|sin(θ)  (68)

With Equations (67) and (68), all the formulas listed in Table 4 can betransferred to format with inputs of V_(α) and V_(β). For example, thetime calculations of the enhanced SVM at m=0 in sector AB become

$\begin{matrix}{T_{1} = {\frac{\sqrt{3}T_{S}}{2V_{D\; C}} \cdot \left( {{\sqrt{3}V_{\alpha}} + V_{\beta}} \right)}} & (69) \\{T_{3} = {\frac{\sqrt{3}T_{S}}{V_{D\; C}} \cdot V_{\beta}}} & (70) \\{T_{0} = {T_{S} - \left( {T_{1} + T_{3}} \right)}} & (71)\end{matrix}$

Inverter with single-shunt current sensing: The connection 780 of athree-phase two-level voltage source inverter 790 and a motor 800 areshown in FIG. 29. As illustrated, the inverter 790 comprises a firstpair of series-connected switches 810, a second pair of series-connectedswitches 820, and a third pair of series-connected switches 830. Each ofthe series-connected pairs 810, 820, and 830 are connected at a nodethat forms an output u, v, w that connects to a respective phase of theload 800. Each of the series-connected pairs 810, 820, 830 also coupletogether at a terminal 850 that couples to a first terminal of a shuntresistor 860 that has a second terminal connected to a referencepotential 870. An amplifier 880 has input terminals coupled to the firstand second terminals of the shunt resistor 860, respectively, wherein anoutput of the amplifier 880 reflects a current conducting through theshunt resistor 860.

The six switching devices of the inverter, which could be MOSFET, IGBTor similar parts, are controlled by microcontroller PWM signals. Themotor windings can be wired in star (as shown) or delta. The enhancedSVM discussed above using either three adjacent active vectors or twonon-adjacent active vectors to synthesize the reference vector is usedto control the PWM to create three-phase sinusoidal waveforms to themotor windings. The shunt resistor R_(shunt) 860 is inserted into theinverter DC link to sense the DC link current. If needed, the amplifier880 is used to amplify the resistor voltage drop which is proportionalto the DC link current. Note that a Hall sensor, a current transformer,or other current sensors can replace the shunt resistor to sense the DClink current.

There are a lot of switching sequence combinations for the new enhancedSVMs, depending on different sequencings of active/zero vectors,splitting of the duty cycles of the vectors, and choice of existing zerovectors (i.e., to choose zero vector {right arrow over (V)}₀ [000], or{right arrow over (V)}₇ [111], or both). It is difficult to list all theswitching sequences here. This section only gives some examples of theswitching sequences, which can be easily implemented using Infineonmicrocontrollers, or other microcontrollers.

Switching sequence design for enhanced SVM: FIGS. 30A and 30B showexamples of 4-segment switching sequences for the enhanced SVM at 890,900, and FIGS. 31A and 31B show examples of 6-segment switchingsequences at 910, 920. FIGS. 32A and 32B show examples of 3-segmentswitching sequences for the enhanced SVM at m=0 at 930, 940, and FIGS.33A and 33B show examples of 5-segment switching sequences at m=0 at950, 960.

Current reconstruction: two/three motor phase currents can bereconstructed by using single-shunt current sensing. In each PWM cycle,inverter DC link current is measured at least twice during two differentactive vector segments to get two motor phase currents. The ADCsamplings are normally triggered near the center of the active vectorsegments to avoid current transitions.

Table 5 shows inverter DC link current of different PWM segments. As anexample, FIG. 34 shows the DC link current I_(DClink) 970 correspondingto the switching sequences 910 shown earlier in FIG. 31A for theenhanced SVM. Two phase currents can be measured at two PWM activevector segments which are more than or equal to T_(min), e.g.:I_(DClink)=−I_(W) during T₂/2 and I_(DClink)=I_(V) during T₃ in FIG. 34if T₂/2≧T_(min) and T₃≧T_(min). With two phase currents, the third motorphase current can be calculated easily because I_(U)+I_(V)+I_(W)=0.

It can be found from FIG. 34 that for the enhanced SVM, it is possibleto take three ADC samplings of inverter DC link current within one PWMcycle to get three motor phase currents directly, if all the threeactive vector segments are longer than T_(min). It will be useful forthe application cases with I_(U)+I_(V)+I_(W)≠0. It is also possible totake only two ADC samplings of the interested motor phase current (e.g.:I_(U) and I_(V) only) directly within any PWM cycle.

TABLE 5 Inverter DC link current of different PWM segments Inverter DClink current PWM Segment I_(DClink) ^(Note 1) Remark Active {right arrowover (V)}₁ [100] I_(U) Take current Vectors {right arrow over (V)}₂[110] −I_(W) sample for {right arrow over (V)}₃ [010] I_(V) motor phase{right arrow over (V)}₄ [011] −I_(U) current {right arrow over (V)}₅[001] I_(W) {right arrow over (V)}₆ [101] −I_(V) Zero {right arrow over(V)}₀ [000] 0 If needed, can Vectors {right arrow over (V)}₇ [111] 0 beused for channel offset calibration ^(Note 1)I_(U), I_(V) and I_(W) arethe currents of motor phases U, V and W, respectively.

To solve the problem as mentioned above, it is possible to approximatethe reference vector {right arrow over (V)}_(ref) in alternative ways asshown in FIGS. 35A and 35B, where n≧0. Using reference vector in sectorA as examples, in FIG. 35A at 980, (1+n){right arrow over (V)}_(ref) isapproximated by two adjacent active vectors just like the existing SVM,and a reverse portion n{right arrow over (V)}_(ref) is approximated bytwo non-adjacent and 120°-separated active vectors; in FIG. 35B at 990,(1+n){right arrow over (V)}_(ref) is approximated by two non-adjacentand 120°-separated active vectors, and a reverse portion n{right arrowover (V)}_(ref) is approximated by two adjacent active vectors. Thealternative solutions shown in FIGS. 35A and 35B use four active vectorsto approximate the reference vector, while the solutions mentionedearlier use three or two. The approximation shown in FIG. 35A can beconsidered a special case of the enhanced SVM at m≧1, and the one shownin FIG. 35B can be considered a special case of the enhanced SVM at m≦0.

The exemplary embodiments described above represent only an illustrationof the principles of the present invention. It is self-evident thatmodifications and variations of the arrangements and details describedherein may be of interest to other specialists. The aim is thereforethat the invention should be restricted only by the scope of protectionof the following patent claims and not by the specific details, whichhave been presented herein on the basis of the description and theexplanation of the exemplary embodiments.

What is claimed is:
 1. A method of performing space vector modulation(SVM) for pulse width modulation (PWM) control for creating alternatingcurrent (AC) waveforms, comprising: generating a reference signal andsampling the reference signal at a sampling frequency to generate aplurality of reference samples; and performing a reference vectorapproximation to synthesize a reference vector associated with at leastone of the reference samples, wherein the reference vector approximationemploys active vectors, one or more zero vectors, and one or more pseudozero vectors in the formation thereof.
 2. The method of claim 1, whereina pseudo vector comprises a combination of two active vectors that havean angle difference therebetween of 180°.
 3. The method of claim 2,wherein the two active vectors that in combination form the pseudovector have a scalar amplitude that is the same.
 4. The method of claim1, wherein a pseudo vector comprises a combination of three activevectors that have an angle difference therebetween of 120°.
 5. Themethod of claim 4, wherein the three active vectors that in combinationform the pseudo vector have a scalar amplitude that is the same.
 6. Themethod of claim 1, wherein the active vectors in the reference vectorapproximation comprise adjacent active vectors.
 7. The method of claim6, wherein a portion of the reference vector is approximated by twoadjacent active vectors, and a remaining portion of the reference vectoris approximated by two non-adjacent active vectors.
 8. The method ofclaim 7, wherein the portion of the reference vector is represented by avariable m, wherein 0≦m≦1, and wherein the remaining portion of thereference vector is represented by 1−m, wherein when m=1, the entirereference vector is approximated by two adjacent active vectors, andwherein when m=0 the entire reference vector is approximated by twonon-adjacent active vectors.
 9. The method of claim 7, wherein thenon-adjacent vectors are separated from one another by 120°.
 10. Acontrol system, comprising: a space vector modulator configured toreceive a plurality of reference signal samples and perform a referencevector approximation to synthesize a reference vector associated with atleast one of the reference signal samples, wherein the reference vectorapproximation employs active vectors, one or more zero vectors, and oneor more pseudo zero vectors in the formation thereof, and wherein thespace vector modulator outputs timing signals based on the referencevector approximation; a pulse width modulation unit configured toreceive the timing signals from the space vector modulator, and outputpulse width modulation control signals based thereon; and a three phaseinverter configured to receive the pulse width modulation controlsignals and generate alternating current waveforms based thereon. 11.The control system of claim 10, wherein a pseudo vector comprises acombination of two active vectors that have an angle differencetherebetween of 180°.
 12. The control system of claim 11, wherein thetwo active vectors that in combination form the pseudo vector have ascalar amplitude that is the same.
 13. The control system of claim 10,wherein a pseudo vector comprises a combination of three active vectorsthat have an angle difference therebetween of 120°.
 14. The controlsystem of claim 13, wherein the three active vectors that in combinationform the pseudo vector have a scalar amplitude that is the same.
 15. Thecontrol system of claim 10, wherein the active vectors in the referencevector approximation comprise adjacent active vectors.
 16. The controlsystem of claim 10, wherein a portion of the reference vector isapproximated by two adjacent active vectors, and a remaining portion ofthe reference vector is approximated by two non-adjacent active vectors.17. The control system of claim 16, wherein the portion of the referencevector is represented by a variable m, wherein 0≦m≦1, and wherein theremaining portion of the reference vector is represented by 1−m, whereinwhen m=1, the entire reference vector is approximated by two adjacentactive vectors, and wherein when m=0 the entire reference vector isapproximated by two non-adjacent active vectors.
 18. The control systemof claim 16, wherein the non-adjacent vectors are separated from oneanother by 120°.
 19. The control system of claim 10, wherein the threephase inverter comprises: a first series-connected switch pair connectedtogether at a node that forms a first phase output; a secondseries-connected switch pair connected together at a node that forms asecond phase output; a third series-connected switch pair connectedtogether at a node that forms a third phase output; a shunt resistorconnected with a first terminal to a bottom node of each of the first,second and third series-connected switch pairs, and a second terminalcoupled to a reference potential; and an amplifier having first andsecond inputs coupled to the first and second terminals of the shuntresistor, respectively, wherein an output of the amplifier reflects acurrent level conducting through the shunt resistor.